First-Principles Hybrid Functional Study of the OrganicâInorganic

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First-principles Hybrid Functional Study of the Organicinorganic Perovskites CHNHSnBr and CHNHSnI 3

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Camille Bernal, and Kesong Yang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp509358f • Publication Date (Web): 26 Sep 2014 Downloaded from http://pubs.acs.org on October 1, 2014

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The Journal of Physical Chemistry

First-principles hybrid functional study of the organic-inorganic perovskites CH3NH3SnBr3 and CH3NH3SnI3 Camille Bernal and Kesong Yang∗ Department of NanoEngineering, University of California San Diego, La Jolla, CA 92093-0448, USA E-mail: [email protected],+1-858-534-2514

∗

To whom correspondence should be addressed

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Abstract We studied the structural and electronic properties of the hybrid perovskites CH3 NH3 SnI3 and CH3 NH3 SnBr3 , as well as their band alignments with respect to the electronconducting TiO2 electrode using first-principles electronic structure calculations. Our hybrid functional calculations yielded band gaps of 1.3 eV and 1.84 eV for CH3 NH3 SnI3 and CH3 NH3 SnBr3 , respectively, which are consistent with experimental values. In addition, our calculations show that the organic cation [CH3 NH3 ]+ does not take part in the formation of the valence band nor the conduction band, and only plays a role in donating one electron in each material. Our band alignment calculations show that introducing substitutional Br dopants for I anions in CH3 NH3 SnI3 could facilitate charge transfer from the hybrid perovskite to the TiO2 electrode, enabling the development of more efficient solar cell architectures.

Introduction Hybrid organic-inorganic perovskites based on the metal halides have emerged as one class of promising light-harvesting materials for next-generation solar cells because of their exceptional properties such as direct band gaps, large absorption coefficients and high carrier mobilities. 1–5 The hybrid halide perovskites are a class of semiconductors of the empirical formula ABX3 . This simple structure comprises a network of corner-sharing BX6 octahedra, in which the metal cation B, often Pb2+ or Sn2+ , is in the center. X represents a monovalent anion (Cl− , Br− or I− ), and A, a monovalent cation, such as the organic molecular [CH3 NH3 ]+ , is chosen to neutralize the overall charge. Miyasaka et al. pioneered applications of the hybrid organic halide perovskites in sensitized solar cells using liquid electrolyte systems. 2 They found that CH3 NH3 PbI3 -based solar cells had 3.8% power conversion efficiency, while the CH3 NH3 PbBr3 -based solar cells had a high photovoltage of 0.96 V. The efficiency of CH3 NH3 PbI3 -based solar cells was later improved to 6.5%, 6 but their performance degraded rapidly due to the hybrid perovskite’s solubility in the liquid electrolyte. A break2 ACS Paragon Plus Environment

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through in durability was the fabrication of CH3 NH3 PbI3 -based all-solid-state solar cells, which demonstrated superior stability and an improved efficiency of 9.7%. 7 A more efficient solar cell based on the meso-superstructured organometal halide perovskite CH3 NH3 PbI3 was recently fabricated, which exhibits a high efficiency of 10.9%. 8 Very recently, hybrid solar cells with ultra-high conversion efficiencies of over 15.0% have been developed using the sequential deposition method based on CH3 NH3 PbI3 4 and the vapor deposition method based on the iodine-chlorine mixed CH3 NH3 PbI3−x Clx , 3 respectively. These two experimental achievements set new records in power conversion efficiency for hybrid organic-inorganic solar cells, and extensive efforts are still in progress to further improve their efficiencies. 9 In spite of significant progress in the development of highly efficient hybrid solar cells, a rising concern is the toxicity of lead in hybrid organolead perovskite-based solar cells, which has potential to inflict harm upon both the human body and the natural environment. In order to develop environmentally-friendly solar cells, it is necessary to find an alternative light-harvesting material that maintains equal or achieves greater power conversion efficiencies than previously mentioned without incorporating toxic lead. Recently, lead-free solid-state organic-inorganic hybrid halide perovskite solar cells based on tin iodide, i.e., CH3 NH3 SnI3 , have been fabricated. 10 The CH3 NH3 SnI3 perovskite has an optical band gap of 1.3 eV, indicating a significant redshift compared to the benchmark light-harvesting material CH3 NH3 PbI3 , whose optical band gap is approximately 1.55 eV. Moreover, by chemical substitution of I by Br in the form of the solid solution CH3 NH3 SnI3−x Brx , the band gap can be tuned to cover a wide range of the visible spectrum. This provides an opportunity to develop lead-free solar cells with high efficiencies, and thus the Sn-based hybrid perovskites could be a promising alternative to the Pb-based light-harvesting materials. Corresponding computational studies have also been carried out to exploit the applications of Sn-based hybrid perovskites in solar cells. For example, Lang et al. studied the chemical trends of the electronic properties in halide perovskites, and proposed that CH3 NH3 SnBr3 could be a promising light-harvesting material because of its appropriate band gap and optical ab-



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sorption. 11 Umari et al. predicted that CH3 NH3 SnI3 would have better electron transport properties than CH3 NH3 PbI3 . 12 Despite prosperous applications of the Sn-based hybrid perovskites in solar cells, a systematic fundamental understanding of their electronic properties and band edge positions is essential for further optimizing their material properties. In this work, by employing hybrid density functional theory (DFT) calculations, we present a comparative computational study for the two hybrid perovskites CH3 NH3 SnI3 and CH3 NH3 SnBr3 . The structural and electronic properties of these two hybrid perovskites, as well as their band alignments with respect to the widely used electron-conducting TiO2 electrode are analyzed. It is found that the organic cation [CH3 NH3 ]+ does not contribute to the formation of the valence band nor the conduction band, and only plays a role in donating one electron in these two materials. We further propose that introducing substitutional Br dopants for I anions in CH3 NH3 SnI3 could be beneficial for facilitating charge transfer from the hybrid perovskite to the TiO2 electrode.

Computational details Our first-principles DFT electronic structure calculations were performed using the Vienna ab-inito simulation package (VASP). 13,14 The projector augmented wave (PAW) potentials were used to treat electron-ion interactions 15 and the generalized gradient approximation (GGA) parameterized by Perdew-Burke-Ernzerhof (PBE) 16 was used for the electron exchange-correction functional. A cut-off energy of 400 eV and a 6 × 6 × 6 k -point mesh centered at the Γ point were used. The convergence threshold for self-consistent-field iteration was set at 10−6 eV, and the atomic positions were fully optimized until all components of the residual forces were smaller than 0.01 eV/˚ A. The density of states (DOS) for each perovskite was calculated by using the tetrahedron method with Blöchl corrections. 17 To account for the underestimation of the band gap in standard DFT calculations, the accurate electronic structures were then calculated using the Heyd-Scuseria-Ernzerhof (HSE06)


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hybrid functional, 18 in which the exact Hartree-Fock (HF) exchange contribution for the hybrid functional was tuned to 46% to match experimental values, as discussed later.

Results and discussion

Figure 1: Geometrical structures of the hybrid cubic perovskites CH3 NH3 SnI3 and CH3 NH3 SnBr3 . The organic [CH3 NH3 ]+ cation was placed along the cube body diagonal, with the median of the C-N bond at the center of the cubic cage.

The hybrid compounds CH3 NH3 SnI3 and CH3 NH3 SnBr3 adopt the cubic perovskite structure at high temperature. 19,20 This structure is constructed of a network of corner sharing SnX6 (X=I, Br) octahedra that encompass an organic monovalent cation, [CH3 NH3 ]+ . It is noted that the organic monovalent cation [CH3 NH3 ]+ is highly disordered and free to rotate at high temperature because the thermal energy surpasses the energy barriers between different stable configurations. 21–23 This indicates that the organic [CH3 NH3 ]+ cation does not form a strong bond with the halide atoms. In this work, following Fabio et al.’s approach, 19 we modeled the geometrical structures of the two compounds by placing the



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[CH3 NH3 ]+ cation along the cube diagonal, with the median of the C-N bond at the center of the cubic cage. The geometrical structures of the two hybrid compounds are illustrated in Fig. 1.

Figure 2: Calculated total energy versus the lattice constant for the hybrid perovskites (a) CH3 NH3 SnI3 and (b) CH3 NH3 SnBr3 . We first estimated the equilibrium lattice constants of the two hybrid perovskite compounds using standard DFT calculations in the frame of the PBE-GGA functional, based on the well-known fact that standard DFT calculations can reasonably predict lattice constants. 24,25 By using the perovskite’s experimental lattice constants as references, we calculated their total energies at a series of different lattice constants. Since the organic [CH3 NH3 ]+ cation does not form a strong bond with the halide atoms, the length of the C-N bond of the organic part remained fixed while the C-H and N-H bonds were fully relaxed in each calculation. The calculated total energies versus the lattice constants of these two hybrid compounds are shown in Fig. 2. The optimized lattice constants from DFT calculations are in good agreement with the experimental values (a = 6.32 ˚ A vs. 6.24 ˚ A for CH3 NH3 SnI3 and a = 5.96 ˚ A vs. 5.89 ˚ A for CH3 NH3 SnBr3 ). 19,26 As expected, the lattice constants of the two compounds are directly proportional to the radius of the halide: with atomic size increasing from Br to I, the perovskite lattice itself must expand to maintain 6 ACS Paragon Plus Environment

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1.3 eV

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Figure 3: Band gap values predicted for CH3 NH3 SnI3 through variation of the Hartree-Fock (HF) contribution. The dashed blue lines indicate the point at which the exchange tuning theoretically reproduces the experimental band gap. Next, we studied the electronic properties of these two hybrid perovskites using hybrid functional calculations. One widespread approach to correct band gaps using hybrid functional calculations is to determine the percentage contribution of the HF exchange by seeking good agreement between the calculated values and the experimental results. 27 In this work, to determine the HF exchange with the greatest potential to produce accurate results, we performed hybrid functional calculations for CH3 NH3 SnI3 with the exact HF exchange contribution set at 0% (a standard DFT calculation), 25%, 30%, and 50%, respectively. Analysis of the resulting data led us to determine the optical band gap with respect to each percent contribution. Referencing the experimental band gap of CH3 NH3 SnI3 (1.3 eV 10 ) alongside a plot of the aforementioned data, the ideal exact hybrid functional contribution was found to be 46%. The varying band gaps versus the percent HF exchange contribution are represented in Fig. 3. To ensure consistency, a 46% contribution was also used to perform the hybrid functional calculations for CH3 NH3 SnBr3 . In addition, we realize that strong 7 ACS Paragon Plus Environment


spin-orbit-coupling (SOC) effects play a significant role in reducing the band gaps of compounds consisting of heavy elements. Recent studies have presented a systematic comparison of the band gap evaluations in Pb- and Sn-based perovskites, respectively, using non-SOC and SOC calculations. 28,29 The results of these studies show a significant difference between the non-SOC and SOC calculations in the Pb-based perovskites (∼ 1.1 eV 28 ) compared to the Sn-based perovskites (∼ 0.35 eV). 29 To further justify our exclusion of the SOC effects in CH3 NH3 SnI3 and CH3 NH3 SnBr3 , we performed our own SOC calculations on these two systems. In each system, the SOC effects further reduce the band gap by approximately 0.3 eV, as expected (see Supporting Information). From this conclusion, we determined that while SOC could not be ignored in Pb-based perovskites, significantly weaker SOC effects in Sn-based perovskites allow us to predict reliable results without incorporating SOC effects.

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Figure 4: (a) Calculated density of states (DOS) and (b-d) partial DOS for CH3 NH3 SnBr3 . The straight, vertical, dashed lines indicate the valence band maximum.


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The calculated total DOS and partial DOS of CH3 NH3 SnBr3 and CH3 NH3 SnI3 are shown in Fig. 4 and Fig. 5, respectively. For the compound CH3 NH3 SnBr3 , standard DFT calculations yielded a band gap of 1.04 eV 19 , showing a significant underestimation with respect to the experimental value of 2.15 eV. 10 In contrast, our hybrid functional calculations predicted a band gap of 1.84 eV, which is much closer to the experimental value than that obtained utilizing standard DFT calculations. The calculated partial DOS plot of the CH3 NH3 SnBr3 compound provided further insight into its electronic properties. Fig. 4a and 4b illustrate that the valence band is mostly composed of Br 4p states while the conduction band is mainly comprised of Sn 5p states. Fig.

4b shows that the Sn 5s

states are predominately located in the valence band, which indicates that the Sn cations are divalent, i.e., Sn2 +, with an electronic configuration of s2 p0 . The partial DOS plots for the organic CH3 and NH3 units of the [CH3 NH3 ]+ cation are presented in Fig. 4c and 4d, respectively. These plots clearly show that the organic CH3 and NH3 introduce three discrete energy levels that fall below the valence band in the energy range -14 to -6 eV. Moreover, the H 1s and C(N) 2p states exhibit strong orbital hybridization, suggesting the formation of strong C-H and N-H covalent bonds. Therefore, our results show that the band gaps of this class of materials are primarily determined by the bond strength of Sn-Br, and that the organic [CH3 NH3 ]+ cation does not take part in the formation of the valence band nor the conduction band; its role is the donation of one electron in the hybrid perovskite material. For the compound CH3 NH3 SnI3 , our hybrid functional calculations yielded a band gap of 1.3 eV, which is in excellent agreement with the experimental value of 1.3 eV. 10 Its total and partial DOS plots are shown in Fig. 5. The valence band of CH3 NH3 SnI3 primarily consists of I 5p states while the conduction band is mainly composed of Sn 5p states, indicating that the bonding strength of Sn-I plays a crucial rule in determining the size of the band gap. The organic [CH3 NH3 ]+ cation shows similar electronic structure features in the hybrid compound CH3 NH3 SnI3 as is observed in the aforementioned CH3 NH3 SnBr3 . Three discrete energy levels are formed below the valence band in the energy range -14 to -7 eV, which



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Figure 5: Calculated density of states (DOS) and partial DOS for CH3 NH3 SnI3 . The straight, vertical, dashed lines indicate the valence band maximum. belong to the organic CH3 (Fig. 5c) and NH3 (Fig. 5d) units. Further analysis on the partial DOS of the organic [CH3 NH3 ]+ cation indicates that the relative positions of the three discrete energy levels in CH3 NH3 SnI3 are an exact match with those in CH3 NH3 SnBr3 . This is because the organic cations in both the hybrid compounds share the same structural configurations, including identical C-N, C-H, and N-H bond lengths and angles. However, it is also noted that the positions of the three discrete energy levels in the hybrid compound CH3 NH3 SnI3 are lower than those in the compound CH3 NH3 SnBr3 by about 0.26 eV. Since these discrete energy levels are highly independent of the halide anions, as discussed above, the orbital positions of the CH3 and NH3 units can be used as energy reference points to determine the relative positions of the valence band maximum between the two organohalide perovskites.


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The large-scale charge separation of electron-hole pairs in light-harvesting semiconductors, i.e., CH3 NH3 SnI3 and CH3 NH3 SnBr3 based on heterojunctions is a key step to converting photon energy to electrical energy using solar cells. This means that the efficiency of a solar cell not only relies on an appropriate band gap, but also on its ability to drive electrons and holes toward the electrodes. The latter can be partially evaluated from the band alignment between the hybrid perovskites and the electrodes. Thermodynamically, the conduction band minimum (CBM) of electron-conducting electrodes should lie below the CBM of the light-harvesting semiconductor, so that the photoinduced electrons can be transferred to the electrode.

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4 . 1 0

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7 . 3 0 Figure 6: Energy level diagram of TiO2 , CH3 NH3 SnI3 and CH3 NH3 SnBr3 . The absolute valence band energies of the hybrid perovskites are computed from first-principles electronic structure calculations. The experimental band gaps of CH3 NH3 SnI3 (1.3 eV) and CH3 NH3 SnBr3 (2.15 eV) are used to determine their conduction band energies. The absolute conduction band energy of -4.1 eV and valence band energy of -7.3 eV for TiO2 are used. 28

Since n-type anatase TiO2 is one widely used electron-conducting electrode material, in order to qualitatively evaluate the ability of the charge transfer in these two hybrid perovskites, we determined their energy-level diagram with respect to the aforementioned 11 ACS Paragon Plus Environment


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electrode, TiO2 , using first-principles slab calculations (see Fig. 6). By aligning the potential profile between the bulk model and the slab model for the hybrid perovskite, we estimated the offset between the vacuum level and the bulk potential for CH3 NH3 SnI3 and CH3 NH3 SnBr3 . 28 The calculated absolute valence band energy was determined to be -5.30 eV for CH3 NH3 SnI3 and -5.51 eV for CH3 NH3 SnBr3 , showing that CH3 NH3 SnBr3 has a lower valence band energy than CH3 NH3 SnI3 by about 0.21 eV. It is worth mentioning that a similar relative position between the valence band energies of CH3 NH3 SnI3 and CH3 NH3 SnBr3 can also be derived from the discrete energy levels of the organic [CH3 NH3 ]+ cation. By aligning the energy levels of the organic [CH3 NH3 ]+ cation in each compound, the valence band energy of CH3 NH3 SnBr3 was found to be lower than that of CH3 NH3 SnI3 by about 0.26 eV, which agrees with our slab calculations. The lower valence band energy of CH3 NH3 SnBr3 versus that of CH3 NH3 SnI3 is primarily because Sn forms stronger bonds with Br than I. Our calculated absolute valence band energies are consistent with the experimental values from ultraviolet photoelectron spectroscopy measurements (-5.30 eV vs. -5.47 eV for CH3 NH3 SnI3 and -5.51 eV vs. -5.54 eV for CH3 NH3 SnBr3 ). 10 Next, we calculated the absolute conduction band energies for CH3 NH3 SnI3 and CH3 NH3 SnBr3 respectively, by using their experimental band gaps (1.3 eV for CH3 NH3 SnI3 and 2.15 eV for CH3 NH3 SnBr3 ). 10 The absolute conduction band energy was estimated to be -4.00 eV for CH3 NH3 SnI3 and -3.36 eV for CH3 NH3 SnBr3 , as shown in Fig. 6. For TiO2 , its absolute conduction band energy of -4.1 eV and valence band energy of -7.3 eV were used. 28 The calculated conduction band energies of CH3 NH3 SnI3 and CH3 NH3 SnBr3 are higher than that of TiO2 , indicating that it is thermodynamically favorable for the electrons to transfer from the hybrid-perovskite light harvester to the TiO2 electrode. It is also noted that the conduction band offset is about 0.1 eV between CH3 NH3 SnI3 and TiO2 , and about 0.74 eV between CH3 NH3 SnBr3 and TiO2 , implying that the light harvester CH3 NH3 SnBr3 has a large driving force for charge transfer in comparison to CH3 NH3 SnI3 . A sizable driving force is beneficial to facilitate both the separation of the photoinduced electron-hole pairs and the charge transfer from the light


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harvester to the electron-conducting electrode. 30 Therefore, to further optimize the power conversion efficiency of CH3 NH3 SnI3 -based solar cells, we propose to shift the conduction band edge of CH3 NH3 SnI3 to higher energy by introducing substitutional Br dopants for I anions. We nevertheless realize that the power conversion efficiency of solar cells is determined by a multitude of factors, including band alignment, band gaps, band bending, and absorber resistance. 31 Hence, besides tuning the band alignment alone, an optimal combination of the band gap and band alignment in the hybrid perovskite CH3 NH3 SnI3−x Brx is expected to significantly improve the efficiency. In fact, Kanatzidis’ research team recently developed a solar cell architecture using CH3 NH3 SnI3−x Brx that shows promising prospects in realizing lead-free, highly efficiently next-generation solid-state solar cells. 10 More detailed computational investigations regarding the influences of Br doping on the band edges and band gap of CH3 NH3 SnI3 , as well as the choice of an optimal doping level are in progress.

Conclusions In conclusion, the structural and electronic properties of CH3 NH3 SnI3 and CH3 NH3 SnBr3 , as well as their band alignments with respect to the electron-conducting TiO2 electrode were studied using first-principles density functional theory calculations. Our hybrid functional calculations yielded a band gap of 1.3 eV for CH3 NH3 SnI3 and 1.84 eV for CH3 NH3 SnBr3 , which are in good agreement with the experimental values. Our results show that the organic cation [CH3 NH3 ]+ does not take part in the formation of the valence band nor the conduction band; its foremost role is the donation of an electron in these two materials. We propose that introducing substitutional Br dopants for I anions in CH3 NH3 SnI3 could be beneficial to facilitate charge transfer from the light absorber to the TiO2 electrode.

Acknowledgement This work is supported by start-up funds at the University of California, San Diego.



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